A great anime, that follows the line of a movie called Blood:The Last Vampire.

Under the care of her adoptive family, Saya Otonashi has been living the life of an anemic and amnesiac, but otherwise ordinary schoolgirl. Saya’s happy life is shattered when she is attacked by a chiropteran, and learns that she is the only one who can defeat them. ("Chiroptera" is the name of the order of biological classification that contains bats, probably the reason for the vampiric creatures being called "Chiropterans".)

Armed with her sword, Saya embarks on a journey with her family, allies and faithful servant, Haji, to rid the world of Chiropterans and rediscover her identity. The course of the journey reveals the background history of the chiropeterans and Saya's very deep past, which extends into the mid-19th century.

The series is initially set in present day (September 2005) Okinawa City (Koza), on Okinawa Island, near the US Kadena Air Base. In the course of the series, Saya visits locales across the world, while fighting enemy chiropterans and searching for her origins.

The anime consists of 50 episodes, and there is word that there will be a second season created in 2008.citation needed

A show about a girl, named Saya(you pronounce it sie-ya) who kills, slices, and dices people with her sword.

But when she loses her memory of the past she has lost the ability to bring pure terror upon any people.
Creatures called Kyropterin (they call them mice) feed on human blood, or animal blood if desperate.
Only Saya has the blood to turn the mice into stone.
The sword is unique, has a blade at the base where Saya cuts her hand with and her blood travels through the whole sword.

A crazy girls who kills anyone she wants to, with a sword!
Movie is called Blood +, look it up on youtube.